The existence of an indecomposable minimal genus two lefschetz fibration

Anar Akhmedov, Naoyuki Monden

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It was shown by Usher that any fiber sum of Lefschetz fibrations over S2 is minimal, which was conjectured by Stipsicz. We prove that the converse does not hold by showing that there exists a genus-2 indecomposable minimal Lefschetz fibration (IMLF for short).

Original languageEnglish (US)
Pages (from-to)29-36
Number of pages8
JournalOsaka Journal of Mathematics
Issue number1
StatePublished - Jan 2021

Bibliographical note

Funding Information:
Acknowledgements. A. Akhmedov was partially supported by Simons Research Fellowship and Collaboration Grants for Mathematicians by Simons Foundation. N. Monden was supported by Grant-in-Aid for Young Scientists (B) (No. 16K17601), Japan Society for the Promotion of Science. First author would like to thank Simons Foundation for supporting this project and the Department of Mathematics at Harvard University for its hospitality. Both authors would like to thank the referee for the valuable comments and suggestions that helped them to improve the presentation of this paper.

Publisher Copyright:
© 2021, Osaka University. All rights reserved.


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